If you are an at will employee, as most are, then, yes, you could be fired for looking for another job. As an at will employee, an employer can fire you for no reason or any reason as long as it is not a discriminatory reason. Your employer may perceive the fact that you are looking for another job as an indication that you are unhappy, unfocused and not loyal to the company. These perceptions, without other facts explaining why you are looking for another job, are sufficient grounds for your termination. You should be particularly careful about accessing job search websites at work, even if its on your lunch hour, as those sites and searches can be viewed by your employer and may be saved on the company’s servers.
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